Dephasing-enabled triplet Andreev conductance

We study the conductance of normal-superconducting quantum dots with strong spin-orbit scattering coupled to a source reservoir using a single-mode spin-filtering quantum-point contact. The choice of the system is guided by the aim to study triplet Andreev reflection without relying on half-metallic materials with specific interface properties. Focusing on the zero-temperature, zero-bias regime, we show how dephasing due to the presence of a voltage probe enables the conductance, which vanishes in the quantum limit, to take nonzero values. Concentrating on chaotic quantum dots, we obtain the full distribution of the conductance as a function of the dephasing rate. As dephasing gradually lifts the conductance from zero, the dependence of the conductance fluctuations on the dephasing rate is nonmonotonic. This is in contrast to chaotic quantum dots in usual transport situations, where dephasing monotonically suppresses the conductance fluctuations.

Figure 1

Sketch of the setup studied in this paper. A normal-conducting chaotic quantum dot (d) coupled to a superconductor (s) via a many-mode contact, and to a normal source reservoir (n), held at an infinitesimal voltage $V$, via a single-mode, spin-filtering QPC. Dephasing is introduced by coupling the dot to a voltage probe (Vp) via a contact supporting $N_{\varphi }$ modes with a tunnel barrier (black rectangle) of transparency ${\Gamma }_{\varphi }$ per mode.

Figure 2

Left panel: probability distribution [Eq. (8)] of the conductance for $N_{\varphi }=1$, for various values of the dephasing rate $g_{\varphi }={\Gamma }_{\varphi }\delta /h$. The curves, in order of decreasing maximum, correspond to ${\Gamma }_{\varphi }=0.2$, 0.4, 0.6, and 1, respectively. The empty squares represent smoothed histograms obtained from 3000 numerically generated scattering matrices for each value of ${\Gamma }_{\varphi }$, for a system where the superconducting contact supports 50 propagating modes. Right panel: the average (solid line) and the standard deviation (dashed line) of the conductance as a function of $g_{\varphi }$. The crosses are results of the numerical simulation.

Figure 3

Left panel: probability distribution of the conductance for $N_{\varphi }⪢1$, for different values of the dephasing rate $g_{\varphi }$. The solid curves, in order of increasing position $G$ of the maximum, correspond to $g_{\varphi }h/\delta =0.05$, 0.5, 1.5, and 10, respectively. The curves are obtained by smoothing histograms from 3000 numerically generated scattering matrices for each value of $g_{\varphi }$, with $N_{\varphi }=100$, for a system where the superconducting contact supports 50 propagating modes. For comparison, we show the distribution for $N_{\varphi }=1$, $g_{\varphi }h/\delta =0.5$ (dashed line). Right panel: the average (solid line) and the standard deviation (dashed line) of the conductance as a function of $g_{\varphi }$. For comparison, the dotted lines show the corresponding functions for $N_{\varphi }=1$.